Left: position (in AU) of the 4 Gyr CHZ inner boundary as a function of the host star mass for the labelled ΔY/ ΔZ values. For each set of mass and ΔY/ ΔZ, the metallicity Z runs from 0.04 at the upper point to 0.005 at the lower one. The initial helium content is obtained from Z and ΔY/ ΔZ as in Eq. (4). To show the effect of the initial helium content, the abscissa of models with high (low) ΔY/ ΔZ are shifted by adding (subtracting) 0.005 M_⊙. Right: same as the left panel, but for the outer boundary. The circles correspond to the computations with T_o = 169 K, while the triangles correspond to those with T_o = 203 K.